Population Size Estimation Using Covariates Having Missing Values and Measurement Error: Estimating Ethnic Group Sizes in New Zealand

We investigate the use of multiple linked lists for population size estimation and to estimate the relationships between covariates appearing on the lists. Over the lists, the covariates aim to measure the same concept. The relationships between the covariates are not fully known because of missing values on the covariates: some cases do not appear in some lists; some cases are on one or more of the lists but have missing covariate values on some of the lists; and some cases are not observed in any list. In earlier work, multiple system estimation has been combined with latent class analysis to give a consensus estimate where an underlying dichotomous categorical covariate is measured differently in different lists. This was applied to ethnicity covariates in New Zealand with two levels, Māori and non-Māori. In this paper, we apply this approach to ethnicity covariates with a larger number of categories, and find that it produces satisfactory results with four categories. We assess the purity of the latent classes using entropy and conditional probability measures. We also examine the evolution of annual estimates from multiple lists (where one list is the population census) over 2013–2020, finding that the estimated latent class proportions are very stable. We assess the impact of disclosure control measures on the outputs.